I have been to Buenos Aires twice, and the best thing about it is the food.  But you can't eat all the time so go to the Recoleta Cemetery it is amazing to get a feel for the passion and the strength of the Argentine people.   around. I would include visits to La Boca and look for the free walking tours around the city center.  They are worth an afternoon.  Finally, I would walk around Puerto Madero One small place that is not on any list and is hard to find is the Centro Cultural Borges museum.  It is in Palermo, and if you are a fan of his, it is worth a visit.  

On the food front, you will find lots of meat everywhere. And it is all good, even the little lunch counters filled with construction workers can be delicious.  However, if you are looking for an inexpensive yet amazing dinner try Sarkis.

Buenos Aires is awesome. Definitely go to Recoleta Cemetery and drink mate on the grass outside. Plaza Italia is a great place to go out at night and Las Terrazas is my favorite club. Make sure you eat Choripan, Alfajores, and finish a whole bottle of wine, after which you might need to take a nap, but that's all good. The best thing to do is find a big park and go for a long walk to get some respite from the urban jungle. Often you'll find live music and such. Good luck on your trip! Hope this helps.